T16-4 φ-宇宙膨胀形式化规范

1. 基础数学对象

1.1 φ-FLRW度量

class PhiFLRWMetric:
    def __init__(self, scale_factor: 'PhiNumber', curvature: int = 0):
        self.a = scale_factor  # 标度因子
        self.k = curvature  # 空间曲率 (-1, 0, 1)
        self.phi = (1 + np.sqrt(5)) / 2
        
    def metric_components(self, t: 'PhiNumber') -> Dict[str, 'PhiNumber']:
        """返回FLRW度量分量"""
        
    def spatial_volume(self) -> 'PhiNumber':
        """计算共动空间体积"""
        
    def conformal_time(self, t: 'PhiNumber') -> 'PhiNumber':
        """计算共形时间"""
        
    def verify_homogeneity(self) -> bool:
        """验证均匀性"""
        
    def verify_isotropy(self) -> bool:
        """验证各向同性"""

1.2 φ-标度因子

class PhiScaleFactor:
    def __init__(self, initial_value: 'PhiNumber'):
        self.a0 = initial_value
        self.phi = (1 + np.sqrt(5)) / 2
        self.evolution_history = [(PhiNumber(0), self.a0)]
        
    def evolve(self, time_step: 'PhiNumber', 
               expansion_rate: 'PhiNumber') -> 'PhiNumber':
        """演化标度因子一个时间步"""
        
    def discrete_evolution(self, n_steps: int) -> List['PhiNumber']:
        """离散Fibonacci演化"""
        
    def redshift(self, t_emit: 'PhiNumber', 
                 t_obs: 'PhiNumber') -> 'PhiNumber':
        """计算宇宙学红移"""
        
    def verify_no_11_constraint(self) -> bool:
        """验证演化历史满足no-11约束"""

1.3 φ-哈勃参数

class PhiHubbleParameter:
    def __init__(self, H0: 'PhiNumber'):
        self.H0 = H0  # 当前哈勃常数
        self.phi = (1 + np.sqrt(5)) / 2
        
    def hubble_rate(self, scale_factor: 'PhiScaleFactor', 
                    t: 'PhiNumber') -> 'PhiNumber':
        """计算给定时刻的哈勃参数"""
        
    def deceleration_parameter(self, a: 'PhiNumber', 
                              H: 'PhiNumber') -> 'PhiNumber':
        """计算减速参数 q = -a*a''/a'^2"""
        
    def hubble_time(self, H: 'PhiNumber') -> 'PhiNumber':
        """哈勃时间 t_H = 1/H"""

2. 动力学方程

2.1 φ-Friedmann方程求解器

class PhiFriedmannSolver:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        self.G_phi = PhiNumber(1.0)  # φ-引力常数
        
    def friedmann_equation(self, a: 'PhiNumber', rho: 'PhiNumber', 
                          k: int, Lambda: 'PhiNumber') -> 'PhiNumber':
        """第一Friedmann方程: H^2 = 8πρ/3 - k/a^2 + Λ/3"""
        
    def acceleration_equation(self, a: 'PhiNumber', rho: 'PhiNumber', 
                            p: 'PhiNumber', Lambda: 'PhiNumber') -> 'PhiNumber':
        """第二Friedmann方程: a''/a = -4π(ρ+3p)/3 + Λ/3"""
        
    def continuity_equation(self, rho: 'PhiNumber', p: 'PhiNumber', 
                           H: 'PhiNumber') -> 'PhiNumber':
        """连续性方程: dρ/dt + 3H(ρ+p) = 0"""
        
    def solve_evolution(self, initial_conditions: Dict, 
                       time_span: Tuple['PhiNumber', 'PhiNumber']) -> Dict:
        """求解宇宙演化"""

2.2 φ-能量密度组分

class PhiEnergyDensity:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def radiation_density(self, a: 'PhiNumber', 
                         rho0_rad: 'PhiNumber') -> 'PhiNumber':
        """辐射密度: ρ_rad = ρ0_rad * a^(-4)"""
        
    def matter_density(self, a: 'PhiNumber', 
                      rho0_mat: 'PhiNumber') -> 'PhiNumber':
        """物质密度: ρ_mat = ρ0_mat * a^(-3)"""
        
    def dark_energy_density(self, Lambda: 'PhiNumber') -> 'PhiNumber':
        """暗能量密度: ρ_Λ = Λ/(8π)"""
        
    def total_density(self, a: 'PhiNumber', 
                     components: Dict[str, 'PhiNumber']) -> 'PhiNumber':
        """总能量密度"""
        
    def equation_of_state(self, component: str) -> 'PhiNumber':
        """状态方程参数 w = p/ρ"""

2.3 φ-熵增与膨胀

class PhiEntropyExpansion:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def universe_entropy(self, a: 'PhiNumber', T: 'PhiNumber') -> 'PhiNumber':
        """宇宙总熵 S ~ a^3 * T^3"""
        
    def entropy_production_rate(self, H: 'PhiNumber', 
                               S: 'PhiNumber') -> 'PhiNumber':
        """熵增率 dS/dt"""
        
    def expansion_from_entropy(self, dS_dt: 'PhiNumber') -> 'PhiNumber':
        """从熵增率计算膨胀率"""
        
    def verify_entropy_increase(self, evolution: List[Dict]) -> bool:
        """验证熵增原理"""

3. 宇宙演化阶段

3.1 φ-暴胀

class PhiInflation:
    def __init__(self, phi_field: 'PhiNumber'):
        self.phi_field = phi_field  # 暴胀子场
        self.phi = (1 + np.sqrt(5)) / 2
        
    def slow_roll_parameters(self, V: 'PhiNumber', 
                           V_prime: 'PhiNumber') -> Dict[str, 'PhiNumber']:
        """慢滚参数 ε, η"""
        
    def e_foldings(self, phi_initial: 'PhiNumber', 
                   phi_final: 'PhiNumber') -> 'PhiNumber':
        """e-折叠数"""
        
    def primordial_spectrum(self, k: 'PhiNumber') -> 'PhiNumber':
        """原初扰动谱"""
        
    def reheating_temperature(self) -> 'PhiNumber':
        """再加热温度"""

3.2 φ-辐射主导

class PhiRadiationDominated:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def scale_factor_evolution(self, t: 'PhiNumber') -> 'PhiNumber':
        """a(t) ~ t^(1/2)"""
        
    def temperature_evolution(self, a: 'PhiNumber', 
                            T0: 'PhiNumber') -> 'PhiNumber':
        """T ~ a^(-1)"""
        
    def neutrino_decoupling(self) -> 'PhiNumber':
        """中微子退耦温度"""
        
    def nucleosynthesis_epoch(self) -> Dict[str, 'PhiNumber']:
        """核合成时期参数"""

3.3 φ-物质主导

class PhiMatterDominated:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def scale_factor_evolution(self, t: 'PhiNumber') -> 'PhiNumber':
        """a(t) ~ t^(2/3)"""
        
    def growth_factor(self, a: 'PhiNumber') -> 'PhiNumber':
        """物质扰动生长因子"""
        
    def matter_radiation_equality(self, Omega_m: 'PhiNumber', 
                                 Omega_r: 'PhiNumber') -> 'PhiNumber':
        """物质-辐射相等时刻"""
        
    def recombination_redshift(self) -> 'PhiNumber':
        """复合红移"""

3.4 φ-暗能量主导

class PhiDarkEnergyDominated:
    def __init__(self, w: 'PhiNumber' = PhiNumber(-1)):
        self.w = w  # 暗能量状态方程
        self.phi = (1 + np.sqrt(5)) / 2
        
    def scale_factor_evolution(self, t: 'PhiNumber', 
                              H0: 'PhiNumber') -> 'PhiNumber':
        """指数膨胀 a(t) ~ exp(Ht)"""
        
    def acceleration_onset(self, Omega_m: 'PhiNumber', 
                          Omega_Lambda: 'PhiNumber') -> 'PhiNumber':
        """加速膨胀开始红移"""
        
    def future_horizon(self) -> 'PhiNumber':
        """未来事件视界"""

4. 观测量计算

4.1 φ-距离测量

class PhiCosmologicalDistances:
    def __init__(self, cosmology: Dict):
        self.cosmology = cosmology
        self.phi = (1 + np.sqrt(5)) / 2
        
    def comoving_distance(self, z: 'PhiNumber') -> 'PhiNumber':
        """共动距离"""
        
    def angular_diameter_distance(self, z: 'PhiNumber') -> 'PhiNumber':
        """角直径距离"""
        
    def luminosity_distance(self, z: 'PhiNumber') -> 'PhiNumber':
        """光度距离"""
        
    def distance_modulus(self, z: 'PhiNumber') -> 'PhiNumber':
        """距离模数"""

4.2 φ-CMB观测量

class PhiCMBObservables:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def acoustic_peaks(self, ell: int) -> 'PhiNumber':
        """声学峰位置"""
        
    def power_spectrum(self, ell: int, 
                      cosmology: Dict) -> 'PhiNumber':
        """CMB功率谱 C_ℓ"""
        
    def phi_modulation(self, ell: int) -> 'PhiNumber':
        """φ-调制效应"""

4.3 φ-大尺度结构

class PhiLargeScaleStructure:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def matter_power_spectrum(self, k: 'PhiNumber', 
                            z: 'PhiNumber') -> 'PhiNumber':
        """物质功率谱 P(k)"""
        
    def correlation_function(self, r: 'PhiNumber') -> 'PhiNumber':
        """两点相关函数"""
        
    def baryon_acoustic_oscillations(self) -> 'PhiNumber':
        """重子声学振荡尺度"""

5. no-11约束效应

5.1 膨胀率限制

class PhiExpansionConstraints:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def max_hubble_rate(self) -> 'PhiNumber':
        """最大哈勃率"""
        
    def forbidden_scale_factors(self, a0: 'PhiNumber') -> List['PhiNumber']:
        """禁止的标度因子值"""
        
    def allowed_redshifts(self) -> List['PhiNumber']:
        """允许的红移值"""

5.2 时间量子化

class PhiTimeQuantization:
    def __init__(self):
        self.phi = (1 + np.sqrt(5)) / 2
        
    def cosmic_time_steps(self) -> List['PhiNumber']:
        """宇宙时间的离散步长"""
        
    def age_quantization(self, n: int) -> 'PhiNumber':
        """量子化的宇宙年龄"""

6. 验证函数

6.1 理论一致性检查

def verify_friedmann_consistency(solver: 'PhiFriedmannSolver', 
                                state: Dict) -> bool:
    """验证Friedmann方程的一致性"""
    
def verify_energy_conservation(evolution: List[Dict]) -> bool:
    """验证能量守恒"""
    
def verify_entropy_increase(entropy_history: List['PhiNumber']) -> bool:
    """验证熵增原理"""

6.2 数值精度检查

def check_evolution_accuracy(numerical: List['PhiNumber'], 
                           analytical: List['PhiNumber']) -> float:
    """检查演化的数值精度"""
    
def check_redshift_consistency(z_calculated: 'PhiNumber', 
                             z_observed: 'PhiNumber') -> float:
    """检查红移计算的一致性"""

7. 关键常数

# 物理常数（φ-单位制）
PHI = (1 + np.sqrt(5)) / 2
H0_PHI = PhiNumber(70)  # km/s/Mpc in φ-units
T_CMB_PHI = PhiNumber(2.725)  # K in φ-units
RHO_CRITICAL_PHI = PhiNumber(8.5e-27)  # kg/m³ in φ-units

# 宇宙学参数
OMEGA_M_PHI = PhiNumber(0.3)  # 物质密度参数
OMEGA_LAMBDA_PHI = PhiNumber(0.7)  # 暗能量密度参数
OMEGA_R_PHI = PhiNumber(9e-5)  # 辐射密度参数

# 特征红移
Z_EQ_PHI = PhiNumber(3400)  # 物质-辐射相等
Z_REC_PHI = PhiNumber(1100)  # 复合
Z_ACC_PHI = PhiNumber(0.5)  # 加速开始

8. 错误处理

class PhiCosmologyError(Exception):
    """宇宙学计算错误基类"""
    
class NegativeScaleFactorError(PhiCosmologyError):
    """负标度因子"""
    
class EntropyDecreaseError(PhiCosmologyError):
    """熵减少（违反第二定律）"""
    
class CausalityViolationError(PhiCosmologyError):
    """因果性违反"""